Compute the weak solution to the problem (a(x)u')' – u = x _for x € (0, 1), u(0) = u(1) = 0 , 1 with a(x) = für x < 1/2, F{4 für æ > 1/2.

Q: If g(t) = (√t 4) (√t + 1), then: g'(4) =

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Q: TRANSCRIBE THE FOLLOWING SOLUTION IN DIGITAL FORMAT

A: Want: To transcribe the given text in digital format

Q: if g'(x) = x(x-5)(x+1)4 , then g has a local maziumum at

A: Given that g'(x)=x(x-5)(x+1)4

Q: Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find r'(1) and s'(4).…

A: our objective is to find the required derivative

Q: 03/05/2021 Worksheet MTH 1410 2. Suppose f(x) is a differentiable function and (x2 + 1)f (x) – 20…

A: Please see the explanation below

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to 8 n = 4 (-x¹ + 22x³ -…

A: (a)How large should n be to guarantee that the Trapezoidal Rule approximation  to is accurate to…

Q: FIND M'(3) = Page 2 of 4 -1 6 2 g(x) • F(x) LET M (x) = F (g(x)) AND V(x) = 9 (f(x)) 6 FIND V'(3) =

A: Step 1: Step 2: Step 3: Step 4:

Q: (7) If f(z) is analytic function show that: (+)rox-4rt =

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Q: 9) Sketch the graph of a function f(x) on the interval (-4,4) with the following properties. f(x) is…

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Q: 4)Given f(x) = 2x/(x2 + 1) a)Find the derivative. b)Find the critical numbers .

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Q: x²+2x=1 then f'(1) is Let f(x) = 2x3+1

A: we have given f(x). And we have to find f'(1)

Q: a) If L-{F(s)} = f(t) and L-1{G(s)} = g(t), and if a and B are constants, then L-1{aF(s) + BG(s)} =…

A: If L[f(t)]=F(s), then f(t) is called the inverse Laplace transform of F(s). That is; f(t)=L-1[F(s)]

Q: Suppose f(2) = 4, f' (2) = 5, f(8) = 8, f' (8) = 2, g(2) = 4, g' (2) = -6, | dH and H(x) = f(x² +…

A: Topic :- Derivative

Q: +1²y=y² If the function u = ln (2¹+2²4 - v² ) then a Su rou + you is

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Q: 8(x) 48. f(x) 2 - x' In Exercises 51–60, show that f(g(x)) = x an dom x - 1 g(x) of 51,fx) = 2r + 1,…

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Q: Find the partial derivative Əz Əx for the function z = 8y²√x.

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Q: not Show that ([0,1]_is in the l' metric d (fig)= (51f6)-96) ³d x) ² fumpluts

A: The given set is X = C[0,1] and the metric defined on X is L2 metric which is defined as  df, g =…

Q: b\ Find the domain of the functions: (1) y = (2) y = = (3)f(x) =

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Q: f'5)%=2 U13)=5, U(3)=7, find (fou)'(3)

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Q: y' = 8|x| = - 8x, x≤0 8x, x>0

A: To find y'' and graph the general shape of f(x), we first need to integrate the given expression for…

Q: 1. Find the third order derivative f"(2) of f(x) = x³. Of" (2) = 1 Of" (2) = 0 Of" (2) = 12 Of"" (2)…

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Q: 3) f (x) = 2 x2 + 4000/x +10 a)Find the derivative . b)Find the critical number(s), if any.

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Q: (e2* ) In(3x+2) Vx' - x -1 Determine f '(x) if f(x)= DO NOT SIMPLIFY!

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Q: O 8e²-4e-4t ○ 4e²¹-8e-4t Ninguna correcta • u = x(4+ y²), x = e³t & y =

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Q: Find f'(x) for f(x) = In(x +x²) with x # 0. Select one or more: a. x* + x² b. 4x + 2 x + x O c. 4x +…

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Q: Suppose that f and f'satisfy the following. X f(x) f'(x) Calculate 2 0 -2 4 15 -3 6 13 2 A) g' (2)…

A: (A) given g(x)=3sin(f(x))

Q: show that the inverse of arotation matrix is transpose,which is also arotation matrix, and it is…

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Q: 3x Let F (x) = In tdt then F'(x) = 9xe - 3xe 6xex - 3x e 3xe - 3x°e 9xe* - 3x'e

A: We use Leibnitz Theorem.